A Lattice structure of Z-soft covering based rough set and its application

Abstract

The aim of this paper is to construct the lattice structure for Z-soft covering based rough set. First, we define an equivalence relation R’ on a universal set to obtain the equivalence classes induced by Z-soft covering-based rough set. Also, we define a relation RS on the family of Z-soft covering-based rough set (TS) to show that the relation RS is a poset on TS. Second, we define two operations join ∨ and meet ∧ on TS. Using these two operations, we prove that every pair of elements of RS has a least upper bound and a greatest lower bound and as a result, TS is a lattice. Finally, we develop a novel Multiple Attribute Group Decision Making (MAGDM) model using Z-soft covering based rough set in medical diagnosis to determine the patients at high risk of chronic kidney disease using the collected data from the UCI Machine Learning Repository.